Question

How many hemispheres with a radius of 3 cm can be produced by melting down a hemisphere with a radius of 12 cm?

• A. 32
• B. 64
• C. 12
• D. 54

Answer 1

Answer:

B. 64

Since the hemisphere is melted and recast, volume is conserved.

Volume of a hemisphere is:

$V=\frac{2}{3}\pi r^3$

Let the number of smaller hemispheres be (n)

$\frac{2}{3}\pi (12)^3$

$n\left(\frac{2}{3}\pi (3)^3\right)$

The common factors $(\frac{2}{3}\pi)$ cancel:

$12^3 = 27n$
$1728 = 27n$
$n = \frac{1728}{27} = 64$